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405 lines
15 KiB
Markdown
405 lines
15 KiB
Markdown
# Double-ended queue
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In a queue, we can only delete elements from the head or add elements to the tail. As shown in the figure below, a <u>double-ended queue (deque)</u> offers more flexibility, allowing the addition or removal of elements at both the head and the tail.
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## Common operations in double-ended queue
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The common operations in a double-ended queue are listed below, and the names of specific methods depend on the programming language used.
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<p align="center"> Table <id> Efficiency of double-ended queue operations </p>
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| Method Name | Description | Time Complexity |
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| ------------- | -------------------------- | --------------- |
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| `pushFirst()` | Add an element to the head | $O(1)$ |
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| `pushLast()` | Add an element to the tail | $O(1)$ |
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| `popFirst()` | Remove the first element | $O(1)$ |
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| `popLast()` | Remove the last element | $O(1)$ |
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| `peekFirst()` | Access the first element | $O(1)$ |
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| `peekLast()` | Access the last element | $O(1)$ |
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Similarly, we can directly use the double-ended queue classes implemented in programming languages:
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=== "Python"
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```python title="deque.py"
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from collections import deque
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# Initialize the deque
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deq: deque[int] = deque()
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# Enqueue elements
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deq.append(2) # Add to the tail
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deq.append(5)
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deq.append(4)
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deq.appendleft(3) # Add to the head
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deq.appendleft(1)
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# Access elements
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front: int = deq[0] # The first element
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rear: int = deq[-1] # The last element
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# Dequeue elements
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pop_front: int = deq.popleft() # The first element dequeued
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pop_rear: int = deq.pop() # The last element dequeued
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# Get the length of the deque
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size: int = len(deq)
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# Check if the deque is empty
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is_empty: bool = len(deq) == 0
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```
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=== "C++"
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```cpp title="deque.cpp"
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/* Initialize the deque */
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deque<int> deque;
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/* Enqueue elements */
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deque.push_back(2); // Add to the tail
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deque.push_back(5);
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deque.push_back(4);
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deque.push_front(3); // Add to the head
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deque.push_front(1);
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/* Access elements */
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int front = deque.front(); // The first element
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int back = deque.back(); // The last element
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/* Dequeue elements */
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deque.pop_front(); // The first element dequeued
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deque.pop_back(); // The last element dequeued
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/* Get the length of the deque */
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int size = deque.size();
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/* Check if the deque is empty */
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bool empty = deque.empty();
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```
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=== "Java"
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```java title="deque.java"
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/* Initialize the deque */
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Deque<Integer> deque = new LinkedList<>();
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/* Enqueue elements */
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deque.offerLast(2); // Add to the tail
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deque.offerLast(5);
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deque.offerLast(4);
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deque.offerFirst(3); // Add to the head
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deque.offerFirst(1);
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/* Access elements */
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int peekFirst = deque.peekFirst(); // The first element
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int peekLast = deque.peekLast(); // The last element
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/* Dequeue elements */
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int popFirst = deque.pollFirst(); // The first element dequeued
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int popLast = deque.pollLast(); // The last element dequeued
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/* Get the length of the deque */
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int size = deque.size();
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/* Check if the deque is empty */
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boolean isEmpty = deque.isEmpty();
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```
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=== "C#"
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```csharp title="deque.cs"
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/* Initialize the deque */
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// In C#, LinkedList is used as a deque
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LinkedList<int> deque = new();
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/* Enqueue elements */
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deque.AddLast(2); // Add to the tail
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deque.AddLast(5);
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deque.AddLast(4);
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deque.AddFirst(3); // Add to the head
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deque.AddFirst(1);
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/* Access elements */
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int peekFirst = deque.First.Value; // The first element
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int peekLast = deque.Last.Value; // The last element
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/* Dequeue elements */
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deque.RemoveFirst(); // The first element dequeued
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deque.RemoveLast(); // The last element dequeued
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/* Get the length of the deque */
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int size = deque.Count;
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/* Check if the deque is empty */
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bool isEmpty = deque.Count == 0;
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```
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=== "Go"
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```go title="deque_test.go"
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/* Initialize the deque */
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// In Go, use list as a deque
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deque := list.New()
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/* Enqueue elements */
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deque.PushBack(2) // Add to the tail
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deque.PushBack(5)
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deque.PushBack(4)
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deque.PushFront(3) // Add to the head
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deque.PushFront(1)
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/* Access elements */
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front := deque.Front() // The first element
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rear := deque.Back() // The last element
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/* Dequeue elements */
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deque.Remove(front) // The first element dequeued
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deque.Remove(rear) // The last element dequeued
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/* Get the length of the deque */
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size := deque.Len()
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/* Check if the deque is empty */
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isEmpty := deque.Len() == 0
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```
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=== "Swift"
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```swift title="deque.swift"
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/* Initialize the deque */
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// Swift does not have a built-in deque class, so Array can be used as a deque
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var deque: [Int] = []
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/* Enqueue elements */
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deque.append(2) // Add to the tail
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deque.append(5)
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deque.append(4)
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deque.insert(3, at: 0) // Add to the head
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deque.insert(1, at: 0)
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/* Access elements */
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let peekFirst = deque.first! // The first element
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let peekLast = deque.last! // The last element
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/* Dequeue elements */
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// Using Array, popFirst has a complexity of O(n)
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let popFirst = deque.removeFirst() // The first element dequeued
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let popLast = deque.removeLast() // The last element dequeued
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/* Get the length of the deque */
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let size = deque.count
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/* Check if the deque is empty */
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let isEmpty = deque.isEmpty
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```
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=== "JS"
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```javascript title="deque.js"
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/* Initialize the deque */
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// JavaScript does not have a built-in deque, so Array is used as a deque
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const deque = [];
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/* Enqueue elements */
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deque.push(2);
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deque.push(5);
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deque.push(4);
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// Note that unshift() has a time complexity of O(n) as it's an array
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deque.unshift(3);
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deque.unshift(1);
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/* Access elements */
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const peekFirst = deque[0]; // The first element
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const peekLast = deque[deque.length - 1]; // The last element
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/* Dequeue elements */
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// Note that shift() has a time complexity of O(n) as it's an array
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const popFront = deque.shift(); // The first element dequeued
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const popBack = deque.pop(); // The last element dequeued
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/* Get the length of the deque */
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const size = deque.length;
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/* Check if the deque is empty */
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const isEmpty = size === 0;
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```
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=== "TS"
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```typescript title="deque.ts"
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/* Initialize the deque */
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// TypeScript does not have a built-in deque, so Array is used as a deque
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const deque: number[] = [];
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/* Enqueue elements */
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deque.push(2);
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deque.push(5);
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deque.push(4);
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// Note that unshift() has a time complexity of O(n) as it's an array
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deque.unshift(3);
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deque.unshift(1);
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/* Access elements */
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const peekFirst: number = deque[0]; // The first element
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const peekLast: number = deque[deque.length - 1]; // The last element
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/* Dequeue elements */
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// Note that shift() has a time complexity of O(n) as it's an array
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const popFront: number = deque.shift() as number; // The first element dequeued
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const popBack: number = deque.pop() as number; // The last element dequeued
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/* Get the length of the deque */
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const size: number = deque.length;
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/* Check if the deque is empty */
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const isEmpty: boolean = size === 0;
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```
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=== "Dart"
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```dart title="deque.dart"
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/* Initialize the deque */
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// In Dart, Queue is defined as a deque
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Queue<int> deque = Queue<int>();
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/* Enqueue elements */
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deque.addLast(2); // Add to the tail
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deque.addLast(5);
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deque.addLast(4);
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deque.addFirst(3); // Add to the head
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deque.addFirst(1);
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/* Access elements */
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int peekFirst = deque.first; // The first element
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int peekLast = deque.last; // The last element
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/* Dequeue elements */
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int popFirst = deque.removeFirst(); // The first element dequeued
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int popLast = deque.removeLast(); // The last element dequeued
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/* Get the length of the deque */
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int size = deque.length;
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/* Check if the deque is empty */
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bool isEmpty = deque.isEmpty;
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```
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=== "Rust"
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```rust title="deque.rs"
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/* Initialize the deque */
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let mut deque: VecDeque<u32> = VecDeque::new();
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/* Enqueue elements */
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deque.push_back(2); // Add to the tail
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deque.push_back(5);
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deque.push_back(4);
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deque.push_front(3); // Add to the head
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deque.push_front(1);
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/* Access elements */
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if let Some(front) = deque.front() { // The first element
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}
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if let Some(rear) = deque.back() { // The last element
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}
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/* Dequeue elements */
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if let Some(pop_front) = deque.pop_front() { // The first element dequeued
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}
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if let Some(pop_rear) = deque.pop_back() { // The last element dequeued
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}
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/* Get the length of the deque */
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let size = deque.len();
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/* Check if the deque is empty */
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let is_empty = deque.is_empty();
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```
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=== "C"
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```c title="deque.c"
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// C does not provide a built-in deque
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```
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=== "Kotlin"
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```kotlin title="deque.kt"
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```
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=== "Zig"
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```zig title="deque.zig"
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```
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??? pythontutor "Visualizing Code"
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https://pythontutor.com/render.html#code=from%20collections%20import%20deque%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%0A%20%20%20%20deq%20%3D%20deque%28%29%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E9%98%9F%0A%20%20%20%20deq.append%282%29%20%20%23%20%E6%B7%BB%E5%8A%A0%E8%87%B3%E9%98%9F%E5%B0%BE%0A%20%20%20%20deq.append%285%29%0A%20%20%20%20deq.append%284%29%0A%20%20%20%20deq.appendleft%283%29%20%20%23%20%E6%B7%BB%E5%8A%A0%E8%87%B3%E9%98%9F%E9%A6%96%0A%20%20%20%20deq.appendleft%281%29%0A%20%20%20%20print%28%22%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%20deque%20%3D%22,%20deq%29%0A%0A%20%20%20%20%23%20%E8%AE%BF%E9%97%AE%E5%85%83%E7%B4%A0%0A%20%20%20%20front%20%3D%20deq%5B0%5D%20%20%23%20%E9%98%9F%E9%A6%96%E5%85%83%E7%B4%A0%0A%20%20%20%20print%28%22%E9%98%9F%E9%A6%96%E5%85%83%E7%B4%A0%20front%20%3D%22,%20front%29%0A%20%20%20%20rear%20%3D%20deq%5B-1%5D%20%20%23%20%E9%98%9F%E5%B0%BE%E5%85%83%E7%B4%A0%0A%20%20%20%20print%28%22%E9%98%9F%E5%B0%BE%E5%85%83%E7%B4%A0%20rear%20%3D%22,%20rear%29%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%87%BA%E9%98%9F%0A%20%20%20%20pop_front%20%3D%20deq.popleft%28%29%20%20%23%20%E9%98%9F%E9%A6%96%E5%85%83%E7%B4%A0%E5%87%BA%E9%98%9F%0A%20%20%20%20print%28%22%E9%98%9F%E9%A6%96%E5%87%BA%E9%98%9F%E5%85%83%E7%B4%A0%20%20pop_front%20%3D%22,%20pop_front%29%0A%20%20%20%20print%28%22%E9%98%9F%E9%A6%96%E5%87%BA%E9%98%9F%E5%90%8E%20deque%20%3D%22,%20deq%29%0A%20%20%20%20pop_rear%20%3D%20deq.pop%28%29%20%20%23%20%E9%98%9F%E5%B0%BE%E5%85%83%E7%B4%A0%E5%87%BA%E9%98%9F%0A%20%20%20%20print%28%22%E9%98%9F%E5%B0%BE%E5%87%BA%E9%98%9F%E5%85%83%E7%B4%A0%20%20pop_rear%20%3D%22,%20pop_rear%29%0A%20%20%20%20print%28%22%E9%98%9F%E5%B0%BE%E5%87%BA%E9%98%9F%E5%90%8E%20deque%20%3D%22,%20deq%29%0A%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E7%9A%84%E9%95%BF%E5%BA%A6%0A%20%20%20%20size%20%3D%20len%28deq%29%0A%20%20%20%20print%28%22%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E9%95%BF%E5%BA%A6%20size%20%3D%22,%20size%29%0A%0A%20%20%20%20%23%20%E5%88%A4%E6%96%AD%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%0A%20%20%20%20is_empty%20%3D%20len%28deq%29%20%3D%3D%200%0A%20%20%20%20print%28%22%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%20%3D%22,%20is_empty%29&cumulative=false&curInstr=3&heapPrimitives=nevernest&mode=display&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false
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## Implementing a double-ended queue *
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The implementation of a double-ended queue is similar to that of a regular queue, it can be based on either a linked list or an array as the underlying data structure.
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### Implementation based on doubly linked list
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Recall from the previous section that we used a regular singly linked list to implement a queue, as it conveniently allows for deleting from the head (corresponding to the dequeue operation) and adding new elements after the tail (corresponding to the enqueue operation).
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For a double-ended queue, both the head and the tail can perform enqueue and dequeue operations. In other words, a double-ended queue needs to implement operations in the opposite direction as well. For this, we use a "doubly linked list" as the underlying data structure of the double-ended queue.
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As shown in the figure below, we treat the head and tail nodes of the doubly linked list as the front and rear of the double-ended queue, respectively, and implement the functionality to add and remove nodes at both ends.
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=== "LinkedListDeque"
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=== "pushLast()"
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=== "pushFirst()"
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=== "popLast()"
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=== "popFirst()"
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The implementation code is as follows:
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```src
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[file]{linkedlist_deque}-[class]{linked_list_deque}-[func]{}
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```
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### Implementation based on array
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As shown in the figure below, similar to implementing a queue with an array, we can also use a circular array to implement a double-ended queue.
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=== "ArrayDeque"
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=== "pushLast()"
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=== "pushFirst()"
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=== "popLast()"
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=== "popFirst()"
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The implementation only needs to add methods for "front enqueue" and "rear dequeue":
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```src
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[file]{array_deque}-[class]{array_deque}-[func]{}
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```
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## Applications of double-ended queue
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The double-ended queue combines the logic of both stacks and queues, **thus, it can implement all their respective use cases while offering greater flexibility**.
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We know that software's "undo" feature is typically implemented using a stack: the system `pushes` each change operation onto the stack and then `pops` to implement undoing. However, considering the limitations of system resources, software often restricts the number of undo steps (for example, only allowing the last 50 steps). When the stack length exceeds 50, the software needs to perform a deletion operation at the bottom of the stack (the front of the queue). **But a regular stack cannot perform this function, where a double-ended queue becomes necessary**. Note that the core logic of "undo" still follows the Last-In-First-Out principle of a stack, but a double-ended queue can more flexibly implement some additional logic.
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